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Antonio has the following data: $\newline$ $14, r, 13, 3, 9$ $\newline$ If the median is $9$ , which number could $r$ be? $\newline$ Choices: $\newline$ $(A)$ $17$ $\newline$ $(B)$ $3$

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Mean, median, mode, and range: find the missing number

Full solution

Q. Antonio has the following data:

\newline

14, r, 13, 3, 9

\newline

If the median is

9

, which number could

r

be?

\newline

Choices:

\newline

(A)

17

\newline

(B)

3

Understand Problem and Data: Step $1$ : Understand the problem and the data given. $\newline$ Antonio has these numbers: $14$ , $r$ , $13$ , $3$ , $9$ . We need to find the value of $r$ such that the median of these numbers is $9$ .
Arrange Numbers for Median: Step $2$ : Arrange the numbers in ascending order to find the median. $\newline$ Since the median is $9$ , and there are $5$ numbers, $9$ must be the third number in the sorted list. This means two numbers must be less than $9$ and two must be greater than $9$ .
Analyze Choices for $r$ : Step $3$ : Analyze the choices given for $r$ . Choices are (A) $17$ and (B) $3$ . If $r = 17$ , the sorted list would be $3, 9, 13, 14, 17$ , making $13$ the median, which is incorrect.
Check Second Choice: Step $4$ : Check the second choice for $r$ . $\newline$ If $r = 3$ , the sorted list would be $3, 3, 9, 13, 14$ . Here, $9$ is correctly positioned as the median.

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